AO map is pixelated. Any way to fix it? (pictures below)
Properties panel > World tab > Gather options : enable Falloff then play with the Distance and Strength values. 

Do your test AO bakes at 5 Samples and when you are happy with the result then up the Samples to 20 or so for the final bake.

Note, enabling or not the Ambient Occlussion option in the World tab will make no difference to the bake. The Gather options will be greyed out but they can still be changed.

Normally AO bakes are greyscale, if that is what you want then put a check against Normalised in the Bake panel.